3. The arc AB of a circle, center O and radius 6 cm, has...

3. The arc AB of a circle, center O and radius 6 cm, has length 4 cm. Find the area of the minor sector AOB. (5 marks) 4. The diagram shows the sector AOB of a circle of radius r cm. The area of the sector is 15 cm² and ?AOB = 1.5 radians. (10 marks) a. Prove that r = 2?5. b. Find, in cm, the perimeter of the sector OAB. The segment R, shaded in the diagram, is enclosed by the arc AB and the straight-line AB. c. Calculate, to 3 decimal places, the area of R.

Transcript

00:01 Okay, so i have in number three, the length of the arc, and arc length is equal to theta times the radius.

00:12 So theta is arc length over radius.

00:17 So in this problem, theta is arc length is four over radius six, so that's two -thirds radiance.

00:29 I'm getting that because i want to find the area of the sector.

00:34 Area of a sector is half r squared theta.

00:39 So that's half six squared times two thirds.

00:45 So 36 divided by 2 is 18.

00:52 So this is 18 times 2 thirds.

00:56 So that is 12 centimeters.

01:00 Meters squared for that area.

01:05 Okay, so that takes care of number three.

01:10 Now to move on to number four, which is a little confusing because it uses similar letters here.

01:19 Okay, so we have a, b, this is r, these are lowercase r's and that's o.

01:29 Okay, so we have a sector, a, o b, the radius is r, the area of the sector is 15 centimeters squared, and angle aob is 1 .5 radiance.

01:51 Okay, so i want to show that the radius is 2 -r -5.

01:56 Okay, so area again is half r squared theta.

02:03 So 15 equals half r squared and the measure of theta is 1 .5.

02:16 I'm going to multiply both sides by 2.

02:20 So i have 30 equals r squared times 1 .5.

02:29 If i divide both sides by 1 .5, i get r squared is 20, so r is the square root of 20, which is 2 radical 5.

02:50 So that takes care of part a.

02:55 Now let's see b, i want to find the perimeter of the sector.

03:02 Okay, so to find the perimeter of the sector, i need the two sides, right? let me just draw that...

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